Home
Class 12
MATHS
If x=a(costheta+thetasintheta) , y=a(sin...

If `x=a(costheta+thetasintheta)` , `y=a(sintheta-thetacostheta)` , prove that `(d^2x)/(d theta^2)=a(costheta-thetasintheta)`, `(d^2y)/(d theta^(2))=a(sintheta+thetacostheta)` and `(d^2y)/(dx^2)=(s e c^3theta)/(a\ theta)`

Text Solution

Verified by Experts

`x=a("cos" theta + theta "sin" theta)`
`rArr (dx)/(d theta) = a(-"sin" theta + theta "cos" theta + "sin" theta)=a theta "cos" theta`
`"and " y = a("sin" theta - theta "cos" theta)`
`rArr (dy)/(d theta) = a["cos" theta- (-theta "sin" theta + "cos" theta)]=a theta "sin" theta`
`"Now " (dy)/(dx) = (dy//d theta)/(dx//d theta) = (a theta "sin" theta)/(a theta "cos" theta) = "tan" theta`
Promotional Banner

Topper's Solved these Questions

  • Continuity and Differentiability

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 5.7|17 Videos

  • Continuity and Differentiability

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 5.8|6 Videos

  • Continuity and Differentiability

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 5.5|18 Videos

  • APPLICATIONS OF INTEGRALS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

  • DETERMINANTS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

If x=a(theta-sintheta) , y=a(1+costheta) find (d^2y)/(dx^2)

If x=a(theta+sintheta) , y=a(1+costheta) , prove that (d^2y)/(dx^2)=-a/(y^2) .

If x=a(theta+sintheta),y=a(1+costheta), Prove that (d^2y)/(dx^2)=-a/(y^2)

If x=a(1+costheta) , y=a(theta+sintheta) , prove that (d^2y)/(dx^2)=(-1)/a at theta=pi/2 .

If x=a(1-costheta) , y=a(theta+sintheta) , prove that (d^2y)/(dx^2)=-1/a at theta=pi/2 .

Find (dy)/(dx), when x=a e^(theta)(sintheta-costheta),y=a e^(theta)(sintheta+costheta)

If x=a(cos 2 theta+2 theta sin 2 theta) " and" y=a(sin 2 theta - 2 theta cos 2 theta) , find (d^(2)y)/(dx^(2)) " at" theta =(pi)/(8) .

If x=2costheta-cos2theta"and"y=2sintheta-sin2theta" Prove that" (dy)/(dx)=tan((3theta)/2)dot

Evaluate: int(1+costheta)/(theta+sintheta)d theta

If x=acos^3theta,y=a sin^3theta then find (d^2y)/(dx^(2))